Normal-exponential-gamma distribution

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Normal-Exponential-Gamma
Parameters μR — mean (location)
shape
scale
Support
PDF
Mean
Median
Mode
Variance for
Skewness 0

In probability theory and statistics, the normal-exponential-gamma distribution (sometimes called the NEG distribution) is a three-parameter family of continuous probability distributions. It has a location parameter , scale parameter and a shape parameter .

Probability density function[edit]

The probability density function (pdf) of the normal-exponential-gamma distribution is proportional to

,

where D is a parabolic cylinder function.[1]

As for the Laplace distribution, the pdf of the NEG distribution can be expressed as a mixture of normal distributions,

where, in this notation, the distribution-names should be interpreted as meaning the density functions of those distributions.

Applications[edit]

The distribution has heavy tails and a sharp peak[1] at and, because of this, it has applications in variable selection.

References[edit]